Propp Circles

A traffic robot follows three rules as it navigates a square grid. SEEK: Follow the directions of other robots. CLAIM: If on an empty space, claim that space. DIRECT: Cyclically send successive visiting robots north, east, south, or west. If robots are continually dropped into the center, the resulting growth is very circular. Jim Propp studied these robots first, as a refinement of the sandpile model.